Egress, Inc., is a small company that designs, pro- duces, and sells ski jackets and other coats. The creative design team has labored for weeks over its new design for the coming winter season. It is now time to decide how many ski jackets to produce in this production run. Because of the lead times involved, no other production runs will be possible during the season. Predicting ski jacket sales months in advance of the selling season can be quite tricky. Egress has been in operation for only three years, and its ski jacket designs were quite successful in two of those years. Based on realized sales from the last three years, current economic conditions, and professional judgment, 12 Egress employees have independently estimated demand for their new design for the upcoming season. Their estimates are listed in the table below. 

       

Employee	Estimated Demand
1	15,000
2	13,500
3	14,060
4	14,300
5	15,700
6	13,500
7	17,500
8	8,000
9	5,000
10	11,000
11	8,000
12	15,000

To assist in the decision on the number of units for the production run, management has gathered the data in the table below. Note that S is the price Egress charges retailers. Any ski jackets that do not sell during the season can be sold by Egress to discounters for V per jacket. The fixed cost of plant and equipment is F. This cost is incurred regardless of the size of the production run.

Variable production cost per unit (C):	$90
Selling price per unit (S):	$100
Salvage value per unit (V):	$56
Fixed production cost (F):	$100,000

Questions

1. Egress management believes that a normal distribution is a reasonable model for the unknown demand in the coming year. Use an Excel spreadsheet to compute the mean and standard deviation of the estimated demands (in the first table) and they will be used for the demand distribution to generate random demand.

2. Use a spreadsheet model to simulate 1000 possible outcomes for demand in the coming year. Considers all production quantities from 7,500 to 12,000 with an increment of 500. Based on these scenarios, compute the expected profit and the standard deviation for each production quantity. (To generate random normally distributed demand, use Excel formula 'NORM.INV(RAND(), mean, standard deviation, 0)')

3. Based on the same 1000 scenarios, how many ski jackets should Egress produce to maximize expected profit? Call this quantity Q. Is Q equal to mean demand or not? If not, why?